If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to that yields consecutive terms of a geometric sequence is an unknown number

Given

We know

Recall that a geometric sequence is in the form

Therefore, once   are consecutive terms,

To find the ratio, for

we know

Therefore,

The ratio is therefore

Therefore, the first three terms in the geometric sequence are 18, 24, 32.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47